Bridge Rotation

[barb]

I need to schedule a bridge rotation for 18 teams, an 8 month rotation, at 4 homes (4 teams/home) where 2 teams get a bye each month
(I understand that 16 teams will have one bye and 2 teams will never have a bye)  My hope is to get as few duplicates during the 8 month time period as possible.
Thank you for any help -- I have been working on the for 2 days now!!!!

[Ian Wakeling]

Does the following work for you?  Teams 7 and 8 are the ones who never have a bye, and will oppose 24 other teams over the 8 months, so the optimum is when they play 7 of the other teams twice and the remaining 10 teams just once, 24 = 2*7 + 1*10.  The corresponding formula for the teams with a bye would be 21 = 2*4 + 1*13.  I believe the schedule below meets both these criteria.  I am guessing you have more than 4 possible venues (1 per team?), so I not tried to get balance for the 4 homes below.

Hope that helps.

             Home 1       Home 2        Home 3         Home 4        Byes
Month 1  ( 5  7  4  6) ( 1  9 16 10) (15 17 12  8)  (3 18  2 13)   (11 14)
Month 2  ( 6  8  3  5) ( 2 10 15  9) (16 18 11  7)  (4 17  1 14)   (12 13)
Month 3  ( 7 15 14 16) (12 13 10  4) ( 1  8 11  5)  (6  9 18 17)   ( 3  2)
Month 4  ( 8 16 13 15) (11 14  9  3) ( 2  7 12  6)  (5 10 17 18)   ( 4  1)
Month 5  (12  5 16  9) (17  7  3 10) (11  2  8  4)  (1  6 14 13)   (18 15)
Month 6  (11  6 15 10) (18  8  4  9) (12  1  7  3)  (2  5 13 14)   (17 16)
Month 7  ( 5 15  4  3) (16  2  1 17) (12 14 18 11)  (8  7  9 13)   ( 6 10)
Month 8  ( 6 16  3  4) (15  1  2 18) (11 13 17 12)  (7  8 10 14)   ( 5  9)